The base of a triangular garden is 5 yards longer than the height, and the area of the garden is 168 square yards. Find the dimensions of the triangle?
word problems
word problems
2 Answers
height= 16 yards
base = 21 yards
Explanation:
Let the height of the triangular shaped garden be h yards. Its base would then be 5+h yards.
Formula for the area of any traingle is
By this formula,
On simplifying this.
Or
h(h+21) -16(h+21)=0
(h+21)(h-16)=0. This means either h-16=0 or h+21=0.
Since h+21=0 would mean h= -21, this cannot be the required solution, because height of the triangle can never be negative. Hence, h-16=0 would give the height of the triangle as h= 16 yards. The dimensions of the triangle would be height = 16 yards and length of the base = 21 yards
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Explanation:
"let the height "=h
"then base "=h+5larrcolor(blue)"5 yards longer"
• " area of triangle "=1/2" base "xx"height"
rArr1/2h(h+5)=168
"multiply both sides by 2"
rArrh(h+5)=336
"express in standard form and factorise"
rArrh^2+5h-336=0larrcolor(blue)"in standard form"
"the factors of - 336 which sum to + 5 are + 21 and - 16"
rArr(h+21)(h-16)=0
"equate each factor to zero and solve for h"
h+21=0rArrh=-21larrcolor(red)"not valid"
h-16=0rArrh=16
"since "h>0" then h = 16"
"base of triangle "=h+5=16+5=21" yards"
"and height "=h=16" yards"
color(blue)"As a check"
"area "=1/2bh=1/2xx21xx16=168" square yards"